The driver of the vehicle, a 28-year-old man, was known to police for committing minor offences but was not on a terrorism watchlist, the sources said. He was arrested at the scene.
One of the students, a young woman, was being treated for serious head injuries.
“For the moment, it is not being looked at as a terrorist incident although it is also not ruled out,” the Toulouse prosecutor said in a statement.
The driver has long suffered from psychological problems and was hospitalized until Dec. 2016, the prosecutor said.
Monday will mark the second anniversary of attacks in Paris that killed more than 130 people.
Earlier this week, French police arrested nine people and another was arrested in Switzerland in coordinated counter-terrorism swoops.